An apparatus for the formation of a dense plasma focus (DPF) was described and characterized in “Characteristics of the Dense Plasma Focus Discharge” by Mather and Bottoms in 1968, one implementation of which is shown in the cross section view of FIG. 1. Independent discovery by Filippov using the geometry of FIG. 6 also occurred in Russia around the same time. The primary difference between the Mather geometry of FIG. 1 and the Filippov geometry of FIG. 6 is the radial to axial geometric aspect ratio and radial vs coaxial plasma initiation. Referring to FIG. 1, a high voltage is applied from a capacitor through a switch to the DPF device, with a positive potential connected to a terminal 18 which is coupled to a cylindrical inner electrode 16, and a negative or ground potential applied to a terminal 20 formed from a cylindrical outer electrode 14 having a central axis 12. The region between the inner and outer electrodes, and downstream of the central electrode, is filled with a working gas which is typically at a fixed pressure and extends throughout the DPF region. The type of working gas is selected based upon the particular application of the DPF. An insulator 22 is disposed between the positive electrode 16 and negative or grounded electrode 14 to isolate the two electrodes, and a refractory (high melting point and heat resistant) insulating disc 21, typically ceramic or glass, is placed on the insulator 22 surface to encourage the initial formation of the plasma 26a on the radial surface of the disc 21 without the high temperature plasma causing the insulator 22 to melt or vaporize. The plasma is formed through the ionization of the gas disposed in the plasma chamber, and the nature of the plasma is determined by the atomic composition of the gas. The plasma 26a is the result of electrons emitted from the negative electrode 14, which are accelerated by the local electric field towards the positive electrode 16. The accelerated electrons strike the insulator surface or collide with neutral gas atoms and/or molecules, generating secondary free electrons. The secondary electrons are further accelerated under the influence of the local electric field, again striking the insulator surface or colliding with the neutral gas, thereby producing further free electrons. This secondary electron emission process continues in a cascade, eventually leading to a complete electrical breakdown through the gas across the insulator surface producing the initial plasma 26a. This statistically driven process must occur nearly simultaneously at all azimuths in order to form a circumferentially uniform plasma extending across the radial extent of the insulator for proper operation. Although the operation polarity of the inner and outer is typically as shown, the polarity may be favorably reversed as long as the initiating plasma 26a is properly formed as described above. The current flowing through the plasma generates a circumferential magnetic B field as shown in FIG. 4a, and this B field exerts a J×B Lorenz force on the particles of the plasma, thereby accelerating the plasma along the Z axis. The magnetic field generated by the radial current varies inversely with radius away from the center electrode, creating a radial gradient in magnetic field. The radial magnetic field gradient results in an axial J×B Lorenz force gradient, which has a largest magnitude near the center electrode. This larger magnitude Lorenz force causes the plasma near the center electrode to accelerate faster than the plasma near the outer electrode, resulting in an accelerated curved surface or plasma front, as shown in the plasma profile progression 26b, 26c, 26d, and 26e of FIG. 1. As the plasma accelerates forward, the neutral gas in front of the plasma surface is shock heated, swept up, and snowplowed forward by the advancing plasma front into an increasingly dense mass of ionized gas atoms, which also experiences radially outward motion due to the curvature of the plasma surface, thereby shedding part of the accumulated mass by the time the plasma front reaches the end of the center electrode 16 at position 26e. When the plasma front begins to advance beyond the tip of the center electrode 16, the return current path from the plasma front to the center electrode begins to include an ionized outer shell of the gas located off the end of the center electrode. The increased magnetic field nearer the axis causes the newly included plasma shell at the end of the electrode 16, as shown in the partial plasma surface 26f to accelerate radially inwards towards the axis, collapsing into a z-pinch zone 28, which generates a very dense plasma focus, causing the emission of radiation and high energy particles; the radiation is typically emitted isotropically whereas the particle emission may occur predominantly along the Z axis. The high energy particles (ions) thus generated propagate forward to couple out of the device, while the counter-propagating particles (electrons) can damage the center electrode through excessive heat formation from inelastic collisions with the electrode, and can also result in the generation of undesired secondary debris from the electrode. While not required for operation of the DPF device, a counter bore 30 is often added to the center electrode to allow for the spatial diffusion of these particles, and the center electrode may also be water-cooled to mediate the heat load from these particles.
FIG. 2 shows a prior art power source for a dense plasma focus device. A source of charge, shown as a current source 42, is coupled to a storage capacitor 46. When the capacitor 46 is charged, a high voltage pulse is delivered from a pulse generator 44 to a low-inductance ignitron-like switch 48, which comprises a trigger terminal proximal to one of the main current carrying terminals. When the high voltage pulse from generator 44 causes an ionic breakdown near this terminal, the ionic discharge spreads across the switch 48, thereby providing a low impedance and completing the circuit between storage capacitor 46 and the DPF device 54. Intrinsic series inductance 50 represents capacitor, switch, and lead inductance between the capacitor 46 and the DPF 54, which can be minimized in any of the many ways known in the prior art, including the use of wide and closely spaced conductors in the high current loop enclosing switch 48, capacitor 46, and DPF 54. The wide conductors reduce the current density carried, thereby reducing the B field generated, and the use of close proximal spacing of these conductors reduces the enclosed area and resulting stray inductance. The DPF 54 generates an enclosed magnetic flux volume with an associated inductance which increases as the plasma front, initially generated at the time of electrical breakdown across plasma initiation surface insulator 21, advances down the Z axis. The initial plasma enclosed flux is shown in the cross section view of FIG. 4a, and the terminal enclosed flux immediately prior to the z-pinch zone 28 of FIG. 1 is shown in FIG. 4b, with the currents shown schematically as arrows in the inner and outer conductors of DPF 10 of FIG. 1, where the dot and x represent the head and tail, respectively, of the circumferential magnetic field vector.
FIG. 3 shows the waveform 60 for current 62 versus time 64 for current 1152 of FIG. 2. The initiator pulse generator 44 produces a high voltage pulse waveform 70 which closes the ignition-like switch 48, thereby starting the plasma formation and motion in the DPF 54, shown by waveform 60. The magnitude of current 62 reaches a peak value 66 in a time 68, thereafter falling off in a damped second order resonance determined by the loss of stored capacitor energy to the plasma and a resonance determined by the time-dependant inductance of the DPF 54, the fixed intrinsic inductance 50 of FIG. 2, and the capacitance of capacitor 46 FIG. 2. In the design of the DPF, it is desired to cause the maximum current 66 to occur at a time 68 which corresponds to the plasma reaching a region immediately before the pinch zone, shown as 26e of FIG. 1. The effect of the radial plasma pinch phase of the operation of the DPF 54 is shown as the drop in current 61 at the pinch time 69, which recovers after the pinch radially rebounds or a new arc forms near the plasma initiation insulator surface 21. By designing the DPF such that the pinch occurs at time 69 shortly following the maximum current level 66 at time 68, the energy of the capacitor 46 is maximally transferred to the formation of the plasma pinch 28. The selection of the size and voltage of capacitor 46, the length of plasma annulus between inner electrode 16 and outer electrode 14, inner electrode axial length, and plasma gas pressure are interrelated in a complicated manner. The time 68 of maximum current 66, which is where the plasma front should be physically close to the radial Z-pinch zone 28 is determined by the inductance 54 of the DPF, which is itself both a function of DPF 10 geometry, as well as a time-dependent function of the DPF inductance as the plasma front moves along the z axis. Additionally, the speed with which the plasma advances is determined by the gas fill pressure in the chamber, as is the optimum plasma pinch radiation or particle generation for a particular gas.
FIGS. 5a, 5b, 5c and 5d show the waveforms of operation for a optimized DPF device. Current waveform 60 of FIG. 3 reaching a maximum current 66 at time 68 corresponds to current waveform 74 of FIG. 5b reaching a maximum shortly before the z-pinch time 75. The current waveform 74 is shown as an initially linear function for simplicity, but may be changed to a higher order function by the effect of the increased accumulated mass in the plasma front during its axial and radial propagation, thereby counteracting the magnetic acceleration force of the plasma, and the loss of mass in the plasma front caused by the plasma front curvature, enhancing acceleration by the magnetic force. The inductance 54 of the device of FIG. 1 is shown in waveform 72 of FIG. 5a, and the inductance 72 would increase linearly with time if the plasma traveled in Z with linear velocity, however as the plasma is accelerating in Z, this causes a non-linear increase in inductance with time. Onset of the radial plasma motion at the end of the center electrode 16 results in an even more rapid increase in the rate of inductance growth, as the driving magnetic field and current density are now increasing with decreasing radius, hence their product (J×B), the accelerating magnetic force, increases quadratically with decreasing radius. Waveform 76 of FIG. 5c shows the displacement z as the plasma accelerates along the Z axis as a function of time. Waveform 77 shows the inner radius of the plasma front constrained by the diameter of the inner electrode 16 until it finally radially collapses shortly before the time 75 the plasma enters the pinch zone 28 of FIG. 1. As is obvious to one skilled in the art, the waveforms of FIG. 5a, 5b, 5c, and 5d are for illustrative purposes only, and change shape and slope with varying gas pressure, geometries, and applied plasma voltages and currents.
FIG. 6 shows the smaller length-to-diameter aspect ratio of the DPF device geometry of Filippov, which includes an axial plasma initiation 92, in contrast with the radial initiation 26a of FIG. 1. Axial plasma initiation is also commonly used in some implementations of DPF 10. In the geometry of Filippov, an inner electrode 82 is formed about an axis 80, and separated from an outer electrode 86 by an insulator 84, whose geometry allows for the formation of an axially-aligned, azimuthally continuous plasma 92 over the exposed surface of the insulator 84, in a process similar to that described earlier for the insulator 21 of FIG. 1. The plasma surface of the insulator 84 may be fabricated from a refractory insulator material, typically a ceramic or glass, as was earlier described for FIG. 1. The plasma 92 initially advances both radially outward towards electrode 86 and axially along 98. Upon reaching the axial extent of the central electrode 82, the plasma front begins to incorporate gas at the end of the center electrode, which is then accelerated radially inward across the front surface of the center electrode 82, and axially beyond the insulator 84, accelerated by the Lorentz force formed by the B field and plasma current density J, as was described for FIG. 1. The advancing plasma 94 accelerates across the front surface of the electrode 82 and accumulates the ambient gas into an azimuthally symmetric pinch zone 90, which results in the generation of high-energy particles 98 mostly along the axis 80 and having a generally isotropic radiation pattern.
The Mather device of FIG. 1 and the Filippov device of FIG. 6 may be viewed as analogs of each other, the primary difference being the axial to radial geometric aspect ratio which determines whether the duration of the initial axial or final inward radial motion of the DPF operation involves the larger fraction of the DPF operational time. For devices operating in similar modes, the device of FIG. 1 includes a z-axis length for axial acceleration of the plasma up to the time of peak current 66 shown in FIG. 2, prior to the radial motion into the pinch zone 28, while the device of FIG. 6 has an equivalent radial distance allowing an optimally selected peak current to be reached prior to the inward radially accelerating plasma front reaching the pinch zone 90. Additionally, the initiation plasma formation insulator geometries may be either axial or radial, such that FIG. 1 may be modified to generate an axial initial plasma, or the initiator of FIG. 6 may be modified to generate a radial initial plasma without loss of function. Both geometries result in a z-pinch zone on axis whereby the accumulated neutral gas, now a plasma, collides on axis with a velocity sufficiently to generate a high temperature and density plasma which generates the high energy particles, primarily axially, and radiation, primarily isotropically.
In the prior art axial geometry of FIG. 1, the inner electrode is maintained at a sufficiently large diameter to reduce the B field in the vicinity of the electrode. This is done to prevent the velocity of the plasma close to the inner electrode and the plasma near the outer electrode from diverging to such a large extent that the plasma tears and separates. When the plasma current flow is interrupted in this manner, the B field causing the plasma acceleration leaks through the tear, ahead of the plasma front, reducing or eliminating the efficiency of the final z-pinch. An electrode geometry is desired which minimizes the tearing of the plasma in a final phase of acceleration while maximizing the resultant radial velocity of the plasma into the pinch zone. Additionally, it is desired to impart an axial component of B field in the z-pinch zone behind the plasma front for axial stabilization of the plasma front immediately prior to the z-pinch zone.